Goal¶

This post aims to introduce how to normalize the observations including the followings:

Min-Max scaling
Standard scaling

Libraries¶

In [53]:

import pandas as pd
import numpy as np
from sklearn.preprocessing import minmax_scale, StandardScaler
import matplotlib.pyplot as plt
%matplotlib inline

import warnings
warnings.simplefilter('ignore')

Create a data¶

In [63]:

df = pd.DataFrame(data=60*np.random.randn(100)+20)
df.describe()

Out[63]:

	0
count	100.000000
mean	22.664418
std	54.655875
min	-123.482962
25%	-13.641444
50%	27.253111
75%	56.597637
max	179.529729

In [64]:

df.hist();
plt.title('Original Data');

Normalizing¶

Min-Max Scaling¶

$$x_{min-max\,normalized} =\frac{x - min(x)}{max(x) - min(x)} $$

In [65]:

data_minmax = minmax_scale(df, feature_range=(0, 1))
pd.DataFrame(pd.Series(data_minmax.ravel()).describe())

Out[65]:

	0
count	100.000000
mean	0.482314
std	0.180375
min	0.000000
25%	0.362498
50%	0.497458
75%	0.594301
max	1.000000

In [72]:

plt.hist(data_minmax);
plt.title('Min-Max Scaled Data');
plt.axvline(x=np.min(data_minmax), ls=':', c='C0', label='Min');
plt.axvline(x=np.max(data_minmax), ls=':', c='C1', label='Max');
plt.legend();

Standard Scaler¶

This scaling assumes that the data is sampled from Normal distribution. $$x_{standard\,normalized} = \frac{x - mean(x)}{std(x)}$$

In [67]:

ss = StandardScaler()
ss.fit(df)
data_standard_scaled = ss.transform(df)

In [68]:

pd.DataFrame(pd.Series(data_standard_scaled.ravel()).describe())

Out[68]:

	0
count	1.000000e+02
mean	3.552714e-17
std	1.005038e+00
min	-2.687426e+00
25%	-6.676092e-01
50%	8.437905e-02
75%	6.239799e-01
max	2.884513e+00

In [88]:

plt.axvspan(xmin=np.mean(data_standard_scaled)-3*np.std(data_standard_scaled), xmax=np.mean(data_standard_scaled)+3*np.std(data_standard_scaled), color='red', alpha=0.05,label=r'$Mean \pm 3\sigma$');
plt.hist(data_standard_scaled);
plt.title('Standard Scaled Data');
plt.axvline(x=np.mean(data_standard_scaled), ls='-.', c='red', label='Mean');
plt.legend();